A theorem of Coleman asserts that if f is an overconvergent U_p-eigenform of weight k>1 such that the valuation of its U_p-eigenvalue is <k-1, then f is classical modular form. In this talk I will discuss variations of Coleman's proof of this theorem, with an eye towards ideas that generalize to higher-dimensional Shimura varieties. Part of this is joint work with Vincent Pilloni.